λ
4

wave lengths › we get the equation = length of the antenna plus

half the length of the windings of the secondary coil.

For a multiplex secondary system, Drude also formulated the following:

"A multiplex antenna (cage antenna), which may be heterogeneous (partly multiplex and partly simple), 'acts' like a simple antenna of a single wire the radius of which is equal to the radius (when the wires are few) or the diameter (when the wires are many) of the mean sectional area (reckoned as a circle) applicable to the total length and enclosed by the antennæ wires.

"The advantage of using multiplex antennæ in the senders in wireless telegraphy resides to some extent in the diminution of the frequency, but more particularly in the increase of radiation. Both these results are best attained by the use of thick antennæ. Multiplex antennæ are therefore advisable on both grounds, since they are able to replace the heavier thick antennæ.

"The checking action of a coil towards alternating current is greater in proportion as the windings are closer, and the less the radius exceeds that of the straight wire conducting the alternating current."

In the sense employed by Drude, this "act" implies, in the first place, that the multiplex antenna is equivalent to a simple antenna of greater radius, in so far as the wave length of the sender is concerned, that is to say, it induces an augmentation of the period. According to the axiom of Poynting and the inalterable relative position of the electric and magnetic lines of force at a greater distance from the sender, it results as a further consequence that the multiplex antennæ effect an increase in the radiation. With regard to these statements of P. Drude, we should like to draw attention to the following remarks by J. Zenneck, which undoubtedly deserve the closest attention. A simple and a multiplex antenna of the same frequency, and whose dimensions of cross section are very small compared with those of length, have in a distance which is great in comparison with the wave lengths, the same field when the current amplitude in both is the same. With the same potential (spark-gap) the current amplitude is much larger in the multiplex than in the single antenna. The relations can best be shown by the following. From the theoretical considerations of Hertz may be derived the following equation for the field intensity E (in the

equatorial plane which is alone to be considered in wireless telegraphy):

in which A represents a constant factor dependent on the system of measurement, the length of the aerial wire, λ the wave lengths, i the current mean value in the antenna, the distance from it, and the index o the amplitude.

When a simple antenna is replaced by a multiplex antenna of the same length, and of the same wire radius, the potential amplitude being given, there are two changes

(a) the frequency and hence the ratio X (b) the current amplitude i

2

The ratio has been discussed by Drude, with the result that in

2

respect of its individual period a multiplex antenna is equivalent to a simplex antenna of a greater radius. Hence it follows that in both l

the ratio has the same value. As is shown by the experimental

2

measurements of Drude, this ratio for a multiplex antenna, the cross section dimensions of which are small compared with those of length, varies only slightly from that of a simple antenna of the same wire thickness.

This ratio consequently plays only a minor part in practice.

But in regard to the current amplitude a comparison of simple and multiplex antennæ of the same length and wire thickness leads. to the following relation :

I.

when the antenna is used as a simple Marconi sender i20 C2

or a secondary system in a loose-coupled Braun arrangement.

II. 40 for antennæ used as secondary systems in close

120

=

coupled Braun arrangements.

Here C indicates the capacity per length unit; the index 1 refers to the multiplex, the index 2 to the simple antenna.

As the capacity per length unit of the multiplex antenna is

1

much larger than that of a simple antenna, it follows that the current amplitude, and hence the amplitude of the electric field intensity E in the case of the multiplex antenna, is also considerably larger than in the case of a simple antenna. In this fact lies the real importance of a multiplex antenna, not in the alteration of the period with its accompanying minute change of the field intensity.

The superiority of multiplex antennæ over the simple forms may also be expressed in the following way. From M. Abraham's publication on wireless telegraphy it follows that the attainment of maximum potential on the upper extremity of the aerial wire is less important than maximum amplitudes of current at the lower end of the antenna. However, according to M. Wien, this current amplitude is nearly proportional to √С12, wherein C1 and C, represent the primary and secondary capacity. Hence the multiplex antennæ act more favourably in consequence of their greater capacity. For the same reason of strengthening the current in the antenna, it is therefore necessary to minimise the primary selfinduction as well, a result at which we have already arrived by another path.

For the current amplitude, Abraham finds the following additional axiom ::

"If, with a given antenna of the capacity C2 (in microfarads), directly coupled with a primary condenser circuit, it be desired to obtain the highest possible increase in the maximum amplitude of the effective waves, the primary self-induction L1 must be selected in accordance with the equation L1 = 6.7 x 105C."

There consequently results an optimum for L, and a corresponding one for the primary capacity C1; any further increase of the latter would excessively augment the radiation and thereby weaken the maximum wave amplitude occurring after half a beat. These considerations, however, are restricted to relatively close-coupled arrangements of sender and receiver. In loose coupling, the chief point to attain is the production of protracted oscillations, even at the expense of the wave amplitude.

1 According to J. A. Fleming (Cantor Lectures on Hertzian Wave Telegraphy, p. 14; London, 1903) the capacity of a multiplex antenna whose component wires lie pretty close together is about VN times (N= number of wires) larger than the capacity of a single antenna of the same length and wire thickness; a multiplex antenna of 50 wires would show approximately 7 (resp. 2.6) times the effect of a corresponding single antenna.

Moreover, as results from Brandes' measurements, with multiple antennæ the amount of the radiation in relation to the existing energy, i.e. the radiation decrement, is greater than with simple antennæ; hence the use of the former ensures better utilisation of the primary energy.

For the so-called "counter capacity," already frequently mentioned, namely, a metallic surface, S, which forms the electrical counterpoise for the antenna of the length 1, Drude finds the equation

in which s represents the "effective" radius in the sense already described.

According to Drude, the different modes of action of the various couplings furnish valuable information on the nature of the indicators to be used in the receiver. The coherer reacts on differences of potential, and therefore is evidently the most suitable indicator when close coupling is used, the chief property of which resides in the production of maximum amplitudes of potential. With loose coupling, however, the integral effect is the main point, so that Rutherford's magnetic indicator seems more suitable in such cases than the coherer. The reason for this is that alterations in the damping make far less difference to the maximum amplitude than to the integral effect; hence when damping is mostly to be considered, the coherer suffers from a certain indifference. For loose-coupled apparatus it is preferable to use an antenna with relatively high self-induction (coils in the vicinity of the belly of the current) in order to prolong radiation.

At great distances, r, the action of the sender on the receiver, diminishes like the amplitude of intensity of the electric and magnetic

1

field, and consequently like The radiation is proportional to the square of the resulting field intensity.

CHAPTER VII.

BRAUN-ENERGY SYSTEMS.

IT has already been stated that the energy available for radiation is determined by CV2, in which expression C represents the capacity and V the discharge potential of the condenser circuit. The dimensions of the capacity per se are subjected to a natural limitation by the length of waves obtainable in practice because of the relatively short masts. Besides, an increase of the capacity at the expense of the self-induction soon reaches a limit. Furthermore, insuperable difficulties, both theoretical and practical, oppose the increase of the discharge potential.

The way out of this dilemma was discovered by Braun in a method of arrangement, the general principle of which is illustrated in fig. 22.

Here, n equal condensers C are connected by n equal selfinductions L in series to a circuit which is closed by the spark-gaps at the moment of discharge. The charging of the condensers, however, is effected in parallel with low potentials only, by means of the large ohmic or inductive resistances W1, W2, W3, which have nothing to do with the oscillations.

The total available energy is therefore

()(V3) = CV2,

and that, too, with an unchanged duration of oscillation, since

C

T=2π/nL=2π √LC,

as for a simple oscillation circuit.

Braun also proves that the spark discharge is equiphasal throughout, and that each spark has only the damping corresponding to the partial potential difference V.